Fix GA4 Cross-Domain Tracking Issue

I have embedded a third-party service for appointment booking into my website. Users start the process on my site (Domain A) and are then redirected to a booking page (external domain) to complete their appointment. Unfortunately, I am facing issues with Google Analytics 4 (GA4) not capturing booking completions or related events, likely due to cross-domain tracking limitations, despite GTM Preview Mode showing that tags are firing correctly.

I need a freelancer to:
- Investigate the cause of this issue
- Provide recommendations for the implementation

Requirements:
- Must be an expert in Google Tag Manager and Google Analytics
- Must have demonstrable experience in cross-domain tracking and CMPs
- (Bonus) experience tracking events in Setmore